Bounds for moments of symmetric square L-functions

2022/09/28 by Gao, Peng
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2209.13882

Abstract

We study the 2k-th moment at the central point of the family of symmetric square L-functions attached to holomorphic Hecke cusp forms of level one, weight κ. We establish sharp lower bounds for all real k ≥ 1/2 unconditionally. Assuming the truth of the generalized Riemann hypothesis, we also obtain sharp lower bounds for all real 0 ≤ k < 1/2 and sharp upper bounds for all real k ≥ 0.

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